Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 14 - Partial Derivatives - 14.7 Maximum and Minimum Values - 14.7 Exercises - Page 1009: 51



Work Step by Step

Need to apply Lagrange Multipliers Method to determine the dimensions of a rectangular box of maximum volume. we have $\nabla f=\lambda \nabla g$ The volume of a box is $f=V=xyz$ and From the given question let us consider $g=4x+4y+4z=c$ Now, $\lt yz,xz,xy \gt =\lambda \lt 4,4,4 \gt$ Simplify to get the values of x,y and z. $y=x,z=x$ $4x+4y+4z=c$ $4x+4y+4z=c$ $ x=\dfrac{c}{12}$ Thus, Box is a cube with edge length: $c=$ $\dfrac{c}{12}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.